Solve for $x$ and $y$ using elimination. ${x+2y = 9}$ ${-x-3y = -13}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {x+2y = 9}\thinspace$ to find $x$ ${x + 2}{(4)}{= 9}$ $x+8 = 9$ $x+8{-8} = 9{-8}$ ${x = 1}$ You can also plug ${y = 4}$ into $\thinspace {-x-3y = -13}\thinspace$ and get the same answer for $x$ : ${-x - 3}{(4)}{= -13}$ ${x = 1}$